Animals ignore you before you found your first city, to give you a chance to explore and find a good spot. Once you found a city, you're fair game.
The town square is a "safe spot" from animals--animals won't see or attack you there, so as you're laying out a city you can stand there to be safe.
The citizens you see standing around at buildings won't be attacked by animals, so you don't have to worry about them.
As for longer-term protection...animals only spawn on undeveloped tiles, not developed ones, so if you fill all undeveloped tiles in and around your city with parks (or slabs, although parks don't have the levelling effect and are easier to build), no animals will be able to spawn and bother you. When you want to build something else, just bulldoze the park and put something else down.